102 LearnersLast updated on May 26th, 2025
Factors of 546
Factors are the numbers that divide any given number evenly without remainder. In daily life, we use factors for tasks like sharing items equally, arranging things, etc. In this topic, we will learn about the factors of 546, how they are used in real life, and tips to learn them quickly.
What are the Factors of 546?
The numbers that divide 546 evenly are known as factors of 546.
A factor of 546 is a number that divides the number without remainder.
The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, and 546.
Negative factors of 546: -1, -2, -3, -6, -7, -13, -14, -21, -26, -39, -42, -78, -91, -182, -273, and -546.
Prime factors of 546: 2, 3, 7, and 13.
Prime factorization of 546: 2 × 3 × 7 × 13.
The sum of factors of 546: 1 + 2 + 3 + 6 + 7 + 13 + 14 + 21 + 26 + 39 + 42 + 78 + 91 + 182 + 273 + 546 = 1344.
How to Find Factors of 546?
Factors can be found using different methods. Mentioned below are some commonly used methods:
- Finding factors using multiplication
- Finding factors using division method
- Prime factors and Prime factorization
Finding Factors Using Multiplication
To find factors using multiplication, we need to identify the pairs of numbers that are multiplied to give 546. Identifying the numbers which are multiplied to get the number 546 is the multiplication method.
Step 1: Multiply 546 by 1, 546 × 1 = 546.
Step 2: Check for other numbers that give 546 after multiplying
2 × 273 = 546
3 × 182 = 546
6 × 91 = 546
7 × 78 = 546
13 × 42 = 546
14 × 39 = 546
21 × 26 = 546
Therefore, the positive factor pairs of 546 are: (1, 546), (2, 273), (3, 182), (6, 91), (7, 78), (13, 42), (14, 39), and (21, 26).
For every positive factor, there is a negative factor.
Finding Factors Using Division Method
Dividing the given numbers with the whole numbers until the remainder becomes zero and listing out the numbers which result in whole numbers as factors. Factors can be calculated by following a simple division method -
Step 1: Divide 546 by 1, 546 ÷ 1 = 546.
Step 2: Continue dividing 546 by the numbers until the remainder becomes 0.
546 ÷ 1 = 546
546 ÷ 2 = 273
546 ÷ 3 = 182
546 ÷ 6 = 91
546 ÷ 7 = 78
546 ÷ 13 = 42
546 ÷ 14 = 39
546 ÷ 21 = 26
Therefore, the factors of 546 are: 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546.
Prime Factors and Prime Factorization
The factors can be found by dividing it with prime numbers. We can find the prime factors using the following methods:
- Using prime factorization
- Using factor tree
Using Prime Factorization: In this process, prime factors of 546 divide the number to break it down into the multiplication form of prime factors till the remainder becomes 1.
546 ÷ 2 = 273
273 ÷ 3 = 91
91 ÷ 7 = 13
13 ÷ 13 = 1
The prime factors of 546 are 2, 3, 7, and 13.
The prime factorization of 546 is: 2 × 3 × 7 × 13.
Factor Tree
The factor tree is the graphical representation of breaking down any number into prime factors. The following step shows -
Step 1: Firstly, 546 is divided by 2 to get 273.
Step 2: Now divide 273 by 3 to get 91.
Step 3: Then divide 91 by 7 to get 13.
Here, 13 is the smallest prime number, that cannot be divided anymore.
So, the prime factorization of 546 is: 2 × 3 × 7 × 13.
Factor Pairs Two numbers that are multiplied to give a specific number are called factor pairs.
Both positive and negative factors constitute factor pairs.
Positive factor pairs of 546: (1, 546), (2, 273), (3, 182), (6, 91), (7, 78), (13, 42), (14, 39), and (21, 26).
Negative factor pairs of 546: (-1, -546), (-2, -273), (-3, -182), (-6, -91), (-7, -78), (-13, -42), (-14, -39), and (-21, -26).
Common Mistakes and How to Avoid Them in Factors of 546
Mistakes are common while finding factors. We can identify and correct those mistakes using the following common mistakes and the ways to avoid them.
Mistake 1
Forgetting the number itself and 1 is a factor
Children might forget to add the given number itself and 1 as a factor. The number itself and 1 are the factors for every number. Always remember to include 1 and the number itself.
For example, in factors of 546, 1 and 546 are also factors.
Factors of 546 Examples
Problem 1
A group of students has 546 toys to distribute evenly. If there are 13 students, how many toys will each student receive?
Each student will receive 42 toys.
Explanation
To distribute the toys equally, divide the total toys by the number of students.
546/13 = 42
Problem 2
A rectangular garden has an area of 546 square meters and a length of 39 meters. What is the width?
14 meters.
Explanation
To find the width of the garden, use the formula,
Area = length × width
546 = 39 × width
To find the width, divide the area by the length.
546/39 = 14
Problem 3
A bakery has 91 cakes and wants to place them evenly on 7 trays. How many cakes will be on each tray?
Each tray will have 13 cakes.
Explanation
To find the number of cakes on each tray, divide the total number of cakes by the number of trays.
91/7 = 13
Problem 4
A classroom has 546 students who need to be divided into groups of 6. How many students will be in each group?
There will be 91 students in each group.
Explanation
Dividing the students by the total number of groups will give the number of students in each group.
546/6 = 91
Problem 5
There are 273 books to be arranged evenly on 13 shelves. How many books will go on each shelf?
Each shelf will have 21 books.
Explanation
Divide the total number of books by the number of shelves.
273/13 = 21
FAQs on Factors of 546
1.What are the factors of 546?
2.Mention the prime factors of 546.
3.Is 546 a multiple of 6?
4.Mention the factor pairs of 546?
5.What is the square of 546?
6.How can children in Philippines use numbers in everyday life to understand Factors of 546?
7.What are some fun ways kids in Philippines can practice Factors of 546 with numbers?
8.What role do numbers and Factors of 546 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Factors of 546 skills?
Important Glossaries for Factors of 546
- Factors: The numbers that divide the given number without leaving a remainder are called factors. For example, the factors of 546 are 1, 2, 3, 6, etc.
- Prime factors: The factors which are prime numbers. For example, 2, 3, 7, and 13 are prime factors of 546.
- Factor pairs: Two numbers in a pair that are multiplied to give the original number are called factor pairs. For example, the factor pairs of 546 are (1, 546), (2, 273), etc.
- Prime factorization: The expression of a number as the product of prime numbers. For example, 546 = 2 × 3 × 7 × 13.
- Multiplication method: A method to find factors by identifying pairs of numbers that multiply to give the original number. For example, using multiplication to find the factors of 546.
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About BrightChamps in Philippines
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
